Question

events a and b are independent if the occurrence of one does not affect the probability of the other occurring. this statement is best represented in symbols by

○p(a|b)=p(a)
○a|b = a
○p(a and b)=p(a)
○a and b = a

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Explanation:

The conditional - probability formula for independent events states that the probability of event A occurring given that event B has occurred is equal to the probability of event A occurring on its own. The notation for this is $P(A|B)=P(A)$. The other options are incorrect interpretations. Option 2 ($A|B = A$) is an incorrect use of set - notation for conditional probability. Option 3 ($P(A\text{ and }B)=P(A)$) is incorrect as $P(A\text{ and }B)=P(A)\times P(B)$ for independent events. Option 4 ($A\text{ and }B = A$) is also an incorrect set - theoretic representation.

Answer:

$P(A|B)=P(A)$